激光雷达与IMU卡尔曼滤波融合MATLAB仿真程序

以下是一个简单的激光雷达与IMU卡尔曼滤波融合的MATLAB仿真程序：

clc;
clear;
close all;

% 模拟真实轨迹
x = 0: 0.01: 10;
y = sin(x);

% 添加高斯白噪声
xp = x + randn(1,length(x))*0.1;
yp = y + randn(1,length(y))*0.1;

% IMU数据
ax = 0.1*sin(x);
ay = 0.1*cos(x);
az = ones(1,length(x))*9.8;
wx = sin(x);
wy = cos(x);
wz = zeros(1,length(x));

% 激光雷达数据
scanAngles = -pi/2:pi/180:pi/2;
scanData = ones(1,length(scanAngles)).*10;
scanData(1:60) = 1*sin(scanAngles(1:60));
scanData(end-60:end) = 1*sin(scanAngles(end-60:end));

% 滤波初始化
q = [1;0;0;0];
gyroBias = [0;0;0];

% 参数设置
deltaT = 0.01;

% 轨迹预测
for n = 1:length(xp)
qPre = q;
gyroBiasPre = gyroBias;
q = qPre + 0.5*quatmultiply(qPre,[0 wx(n) wy(n) wz(n)])'*deltaT;
q = q./norm(q);
accCorrect = [0 ax(n) ay(n) az(n)];
accCorrect = quatrotate(quatconj(qPre),accCorrect./norm(accCorrect));
gyroBias = gyroBiasPre + accCorrect(2:4)'*deltaT;
H = [zeros(1,3) scanData(n)*cos(scanAngles); zeros(1,2) scanData(n)*sin(scanAngles)];
y = [accCorrect(2:4)'; scanData(n)*cos(scanAngles); scanData(n)*sin(scanAngles)];
R = diag([0.01 0.01 0.01 ones(1,length(scanAngles)).*0.01]);
K = (eye(7)+[zeros(3) -0.5*quat2dcm(qPre)*(deltaT^2);zeros(4,3) eye(4)*deltaT]*[zeros(3) zeros(3,4);zeros(4,3) -skewSymmetric(wx(n),wy(n),wz(n)))'...
)\[eye(4) zeros(4,3)]'; % 计算卡尔曼增益
q = quatmultiply(q,K(1:4,:)*([accCorrect(2:4)-gyroBias;0]+K(5:7,:)*(y-H*K(1:4,:)*[0;gx;gy;gz])-quatmultiply(q,[0;wx(n);wy(n);wz(n)])'*deltaT)');
q = q./norm(q);
gyroBias = gyroBias + K(5:7,:)*(y-H*K(1:4,:)*[0;gx;gy;gz]-quatmultiply(q,[0;wx(n);wy(n);wz(n)])'*deltaT);
end

% 绘制结果
figure;
subplot(221); plot(xp,yp); title('Real Path');
subplot(222); plot(1:length(ax),ax,1:length(ay),ay,1:length(az),az); title('IMU Data');
subplot(223); plot(scanAngles,scanData); title('Lidar Data');
subplot(224); plot3(yp,xp,zeros(size(xp))); title('Raw Data');
hold on
for i = 1:10:length(xp)
r = quatrotate(q',[0 1 0]);
plot3(yp(i)+r(2),xp(i)+r(1),r(3),'r.');
end

% 定义函数计算哈米尔顿矩阵
function H = hamilton(q)
H = [q(1), -q(2), -q(3), -q(4);
q(2), q(1), -q(4), q(3);
q(3), q(4), q(1), -q(2);
q(4), -q(3), q(2), q(1)];
end

% 定义向量叉乘函数
function S = skewSymmetric(wx,wy,wz)
S = [0 -wz wy;
wz 0 -wx;
-wy wx 0];
end